determining project characteristics and critical path by a new approach based on modified nwrt method and risk assessment under an interval type-2 fuzzy environment

Considering the important role of risks in real-world projects and the ability of interval type-2 fuzzy sets (it2fss) to tackle uncertainty, this study introduces a new approach to consider risks and the correlation among risk factors by subjective judgment of experts on the probability and impact under it2fss. furthermore, a new impact function used for considering the correlation among the risk factors is extended under an it2f environment. moreover, a new subtraction operator is introduced for the critical path analysis. the node-weighted rooted tree (nwrt) method is modified based on the proposed new operator to avoid producing negative number for characteristics of each activity. in addition, in order to deal with the uncertainty of the projects, nwrt method is developed under the it2fss. finally, to illustrate the validity and capability of the proposed method, two examples derived from the literature are solved and compared.